x = 0m and y = 0.96m
For a system of masses, the center of mass of these masses is the point at which the masses can be thought of as being most concentrated.
For the four objects, the coordinates of the center of mass G(x, y) is given by;
x = (m₁x₁ + m₂x₂ + m₃x₃ + m₄x₄) / M -----------------(i)
y = (m₁y₁ + m₂y₂ + m₃y₃ + m₄y₄) /M -----------------(ii)
Where;
m₁, x₁ and y₁ = mass, x-position and y-position of object 1
m₂, x₂ and y₂ = mass, x-position and y-position of object 2
m₃, x₃ and y₃ = mass, x-position and y-position of object 3
m₄, x₄ and y₄ = mass, x-position and y-position of object 4
M = the total mass of the objects
From the question;
m₁ = 1.91kg
x₁ = 0 (since it is located at the y axis)
y₁ = 2.95m
m₂ = 3.05kg
x₂ = 0 (since it is located at the y axis)
y₂ = 2.49m
m₃ = 2.60kg
x₃ = 0 (since it is located at the y axis)
y₃ = 0
m₄ = 4.05kg
x₄ = 0 (since it is located at the y axis)
y₄ = -0.504m
M = m₁ + m₂ + m₃ + m₄ = 1.91 + 3.05 + 2.60 + 4.05
M = 11.61kg
Substitute these values into equations (i) and (ii) as follows;
x = ((1.91 x 0) + (3.05 x 0) + (2.60x0) + (4.05x0)) / 11.61
x = 0 / 11.61
x = 0
y = ((1.91 x 2.95) + (3.05 x 2.49) + (2.60x0) + (4.05x-0.504)) / 11.61
y = (5.6345 + 7.5945 + 0 - 2.0412) / 11.61
y = (11.1878) / 11.61
y = 0.96m
Therefore the center of mass of these objects is at x = 0m and y = 0.96m
